The New Sudoku Players' Forum

[Leren]

Some more tidy ups. The only cell with a + sign should be the second ab cell (r3c5) with the + on the RHS. Leren

[rjamil]

Hi Leren,

Some more tidy ups. The only cell with a + sign should be the second ab cell (r3c5) with the + on the RHS. Leren

Did you mean that following Types 9A, 9B & 9C?

Code: Select all

Type 9A                             Type 9B:
-b -b -b  | . +/b .  | .  .  .          -b -b -b  |+b +/b +b | .  .  .
 . ab  .  | . +a/ .  | .  .  .           . ab  .  | / +a/ /  | .  .  .
 .  .  .  | . +ab .  | .  .  .           .  .  .  | / +ab /  | .  .  .
----------+----------+---------         ----------+----------+---------
 .  .  .  | .  /  .  | .  .  .           .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .           .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .           .  .  .  | .  /  .  | .  .  .
----------+----------+---------         ----------+----------+---------
 .  .  .  | .  /  .  | .  .  .           .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .           .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .           .  .  .  | .  /  .  | .  .  .
SL a and b Line wise                    SL a Line wise and b Box wise

Type 9C:
 .  .  .  | .  /  .  | .  .  .
 . ab  .  | . +a  .  |-b -b -b
 /  /  /  | / +ab /  |+b +b +b
----------+----------+---------
 .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .
----------+----------+---------
 .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .
SL a Line wise and b Group Line wise

R. Jamil

[Leren]

Code: Select all

Type 8A:                            Type 8B:
-b -b -b  | .  b  .  | .  .  .       -b -b -b  | /  b  /  | .  .  .
 . ab  .  | .  /  .  | .  .  .        . ab  .  | a  a/  a | .  .  .
 a  a  a  | /  ab+/  | /  /  /        .  .  .  | / ab+ /  | .  .  .
----------+----------+---------      ----------+----------+---------
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
----------+----------+---------      ----------+----------+---------
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .
 .  .  .  | .  /  .  | .  .  .        .  .  .  | .  /  .  | .  .  .

Here is how I would write the exemplars for Types 8A and 8B. Only r3c5 has a + sign to indicate that it may hold digits other than a & b. It would be good if example puzzles can be made that have these moves in them.

A problem I'm having with these exemplars is how can they can come about. For example in Types 8A & 8B how can r2c5 not hold a b ? Presumably it must be in sight of a cell with a clue or solved b in it, but the only ones I can think of would eliminate some of the other b's in the exemplars. So it may be that these exemplars are consistent, but impossible to come about in practice.

Types 9A & B appear to have similar problems and Type C makes no sense, since the b in r3c5 is the only b in Column 5.

Leren

[StrmCkr]

some of the initial eliminations for the type 8 that was removed, could have stayed.

the exemplar don't necessarily assume BLR is applied, the eliminations are applicable with or without it, that being said.

pretty sure
we opted to ommit these in the main document as the underlying pattering was already included with in the main type class: there was a 2ndary covering file that had all the combination types listing min/max arrangements as supplementary reading but Ronk removed and i didn't have a backup.

8a8B : these are both Type 4a & 4b combined with class 6a & 6b as minimal arrangements when applying transformations.

type class 9) similar concerns plus the questions raised by Leren

but im not beyond adding these into the main document: if the general consensus is they should be covered.

but on-honestly this documentation was meant as a generalized code check not a case based id generation: ie the whole 81 * 3 * 3 ~ test cases.

m: wing is: Local - Sector = Local - Local = Sector
m: Ring is : Local - Sector = Local - Local = Sector - first Local

[Hajime]

Are all M-wings the same as an AIC with length of 4 (grouped) cells?

[StrmCkr]

Three strong links two weak links, 2 digits start must be a bivavle => M wing

AIC type 1; (length 5)

(A=B) - (bbb = B) - (a=aaa) => peers of start and end exclude a.

If end and start are peers, we have a M ring. ( Lenght 6 to indicate loop)=>
Peers of start and end are excluded
Ba are locked to cell exclude all other canddiate
Peers of B&bbb are excluded for b.

Notes.
B&a overlap on cell.
Brackets indicate strong link for the sector

At Least one of each letters of the following need to be present
bbb, aaa (which is where group links occupy)

Does that help?

[Hajime]

Does that help?

Yes, thank you. You measure the length of a AIC in links, not in cells.

[Hajime]

One more question. Example Puzzle 143 of P.O. at http://forum.enjoysudoku.com/puzzle-143-t41738.html

Code: Select all

   +------------+------------+---------------+ 
   |458  568  7 |3468  36  9 | 68    2    1  | 
   |a48   3   1 |  5   2  b68|6789 4789  4789| 
   | 9    2 d468|c468  7   1 |  3    5    48 | 
   +------------+------------+---------------+ 
   | 34  79   5 |3679  8  267|  1   479  2479| 
   | 6  1789 489| 179  59 257| 789   3  24789| 
   | 2  1789 389|1379  39  4 |  5   789   6  | 
   +------------+------------+---------------+ 
   | 1  5689  2 |6789 569  3 |  4   789  5789| 
   | 7  5689 689|  2   4  568| 89    1    3  | 
   |358   4  389| 789  1  578|  2    6   5789| 
   +-----------------------------------------+ 

AIC Type 2 [length 5] (4)(4=8)r2c1-(8=6)r2c6-6-r3c4=6=r3c3 => (-4)r3c3
If r2c1 is not a 4, then ... then r3c3 is a 6, so r3c3 can never be a 4.


Because it is an AIC Type 2 it is not a M-wing ??

[Leren]

Hajime wrote : Because it is an AIC Type 2 it is not a M-wing ??

If you look at the exemplars, an M Wing is an AIC on just 2 digits, labelled a and b. There is always a base cell that contains only a and b, which appears in Box 1 in the exemplars. There is an auxiliary cell that contains a, b and possibly other digits, so in the exemplars it's labelled ab+, and appears in Box 2 or Box 4 in the exemplars. There is a Strong link in the base cell, a weak link in the auxiliary cell and various arrangements of a's and b's that allow the various eliminations to be produced.

Leren

[StrmCkr]

aic don't use cells.

they use digits as logic gates of XOR (à and ! A) where not a is b

size class is measured in links.

Forcing chains ie niceloops use cells as BB ploting in other words cellular Atama and are implications so there is a diffrence despite what they might look like.

[rjamil]

Hi Leren and StrmCkr,

A problem I'm having with these exemplars is how can they can come about. For example in Types 8A & 8B how can r2c5 not hold a b ? Presumably it must be in sight of a cell with a clue or solved b in it, but the only ones I can think of would eliminate some of the other b's in the exemplars. So it may be that these exemplars are consistent, but impossible to come about in practice.

Types 9A & B appear to have similar problems and Type C makes no sense, since the b in r3c5 is the only b in Column 5.

Leren

Many thanks for providing your doubts. After more thinking, I now realized that, M-Wing Type 8A, 8B, 9A, 9B and 9C, are come into my mind by seeing M-Ring Type AB move.

In M-Wing Type 9C, SL ar23c5 is present in column 5; and, SL br3c5 and r3c789 is present in row 3. value 'b' may be present any where in r12c456.

Actually M-Wing Type 8A, 8B, 9A, 9B and 9C moves; similar to as M-Ring Type AB move, are all degenerative cases that may be found, at least, before Locked Candidate Type 2 (Claiming) move.

R.Jamil

[StrmCkr]

Actually M-Wing Type 8A, 8B, 9A, 9B and 9C moves; similar to as M-Ring Type AB move, are all degenerative cases that may be found, at least, before Locked Candidate Type 2 (Claiming) move.

not the ring cases,

they are combination of the non-ring types using minimal sets instead of the maximal as presented.

all your doing is cycling the strong link types, in row,col,box: there is overlap to where cases of minimal construct overlap a maximal case and you can use either sector effectively.

when everything in a band the "extra" eliminations are more then likely to be seen as BLR, doesn't mean the aic cannot exclude those but it wont be seen in a hierarchy based system.

all your code needs to worry about is:
bivalve - strong link {type 1,3} - strong link {type 1,2}

where the "-" is the sector share by the previous and next link.

why those limitations? there is a digit exchange between the last two strong links that can only work with the single end point strong links for the digits to have the same cell.